The phase diagrams of chains and ladders of (La,Y,Sr,Ca)14Cu24O41
T.Vuletića, T.Iveka, B.Korin- Hamzića, S.Tomića, B.Gorshunov b,c, M.Dressel b, J.Akimitsu d
a Institut za fiziku, Zagreb, Croatia
b1.Physikalisches Institut, Universität Stuttgart, Germany
c General Physics Institute, Russian Academy of Sciences, Moscow, Russia
d Department of Physics and Mathematics, AoyamaGakuinUniversity, Kanagawa, Japan
The phase diagrams of the intrinsically hole doped spin-ladder and chain composites (La,Y,Sr,Ca)14Cu24O41are reviewed. For the underdoped materials (La,Y)y(Sr,Ca)14-yCu24O41the phase diagram is built only for the chains, since they contain all the holes, hole count= 6 − y per formula unit, f.u. For the fully doped Sr14−xCaxCu24O41, 6 holes per f.u, the phase diagrams are built separately for the chains and for the ladders which also contain holes. While different ground states are identified, like charge-density wave (CDW), superconductivity (SC) and antiferromagnetism, we also point out the correlations between the phase diagrams of the two families, as well as of the two subsystems. These have to be considered when discussing the nature of SC or CDW.
In the quasi-one-dimensional (quasi-1D) systems superconductivity is always in competition and/orcoexistence with other collective electronic ground states, like charge and spin-density waves [1]. Thiscompetition appears also in the quasi-1D (La,Y,Sr,Ca)14Cu24O41, consisting of cuprate spin-chains and spin-ladders, which have attracted muchattention, mainly because they represent the first superconducting copper oxides with a non-square lattice. Inthe case of quasi-1D cuprates experiment was preceded by a theoretical idea that, in an isolated holedopedtwo-leg ladder, the spin-gap will occur and lead to the hole-pairing on the ladder rungs,and eventually to superconductivity, although in competition with a charge-density wave [2]. In addition tosuperconductivity [3], both the gapped spin-liquid [4] and charge-density wave states [5-7] have beenobserved in the intrinsically hole doped spin-ladders of Sr14−xCaxCu24O41. The relevance of these states to the nature ofsuperconductivity is still subject of intensive discussion. In order to catalyze this process we have used ourcharge response studies, as well as many results reported in the literature, to assemble comprehensivephase diagrams of (La,Y)y(Sr,Ca)14−yCu24O41materials as a function of La,Y content and of Sr14−xCaxCu24O41 materials as afunction of Ca content [8].
Stoichiometric reasons limit trivalent La,Y substitution for divalent Sr, Ca to a maximum of six per f.u., which equals to the total hole count nh= 6 per f.u. An undoped Cu-site is characterized by a spin S = 1/2 of the Cu2+ ion, while a hole doped site may be regarded as a Cu3+ ion. Here, the spin S = 0 is observed because a Zhang-Rice singlet forms [9]. In this manner the hole and spin arrangements becomecomplementary within the chains or ladders. The distribution of holes between the ladders and chainsdepends on the La,Y substitution level. Even when La,Y= 0, it depends on Ca substitution [10,11] andon temperature and/or pressure, i.e.under pressure ladder hole count increases, whilethe holes back-transfer into the chains at low temperatures [12,13]. Based on theabove, quasi-1D cuprates are separated into underdoped (La,Y)y(Sr,Ca)14−yCu24O41and fully doped Sr14−xCaxCu24O41.
In the underdoped (La,Y)y(Sr,Ca)14-yCu24O41 (nh= 6-y) the ladders contain no holes and have a spin-gapped ground state, while the holes are found onlyin the chains, up to nh= 5. When most, or all, of the holes are removed from the chains (for 5≤y≤6) an antiferromagnetic (AF) order of ferromagnetic chains may be established, Fig.1, left panel. For higher hole counts, short range AF correlations persist up to y≤2, and give way to an AF dimers phase which exists at short scales for 0.1≤y≤2. The chains in (La,Y)y(Sr,Ca)14-yCu24O41 behave as one-dimensional disorder-driven insulators, up to y = 1. Presumably, the number of holes in the chains can not be over 5, and for y<1, the additional holes should enter in the ladders [14]. As we show in the right panel of Fig. 1, only in the chains of the fully doped Sr14-xCaxCu24O41, (at lowest temperatures, where there can be more than 5 holes in the chains) AF dimers establish two-dimensional (2D) long-range ordered pattern, to which a charge-ordered ground state is associated (CO-AFdimers).
Since Sr14-xCaxCu24O41 have nh= 6, around one hole (already for x=0 and increasing for x>0) is found in the ladders, Fig. 2. The spin-gap of the undoped ladders persists with this hole transfer and seems to be present when superconductivity (SC) appears under pressure in x>10 materials [3,13]. Early theory for ladders based a mechanism for SC on this spin-gap [2]. However, since the pressure increases the hole count and induces 2D charge transport in the ladder layers [8], it is also debatable that SC in the ladders may be related to SC in layered cuprates. At ambient pressure charge-density wave (CDW) was identified as a ground state for 0≤x≤9 [7,8].A sinusoidalcharge modulation, with fivefold periodicity was directly observed for x=0 [15]. It is striking that CO-AFdimers in the chains, and CDW in the ladders are suppressed with increasing x by the similar rate, and, finally, for highest x both subsystems undergo separate AF-orderings. This correlation is only one of the strong indications thatthe observation of CDW up to x=12 and up to 700 K [6] should be regarded as highly controversial. Rather unconventional nature of CDW in the strongly correlated system of the ladders is recognized in the observation of an insulator-to-insulator phase transition and of CDW 2D anisotropic response in ac-fields. In addition, contradictory results are reported regarding nonlinear effects in dc-fields [8], however they all indicate that sliding CDW conductivity is debatable.
A density wave identified in the ladders, as opposed to CO in chains, belongs to the class of broken symmetry patterns, which is theoretically predicted for strongly correlated lowdimensionalelectron systems; however its precise texture and nature is still an open issue. As for superconductivity, the presence ofthe spin gap in the normal state points towards d-wave symmetry and magnetic origin of the attractive interaction. However, there isa finite density of mobile quasi-particles that appears for high Ca contents and increases with pressure, concomitantly with increasedtwo-dimensionality and metallicity. For this reason the superconductivity in the doped ladders of Sr14−xCaxCu24O41 which occursunder high pressure cannot simply be a stabilization of the d-wave expected for a pure single laddersystem.
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